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Consider X ={1,2 }. The number of different ordered pairs(Y,Z) that can be formed such that Y and Z are subsets of X and Y intersection Z is empty, is?.. Please, solve this manually, means i need those subsets and ordered pairs..

Consider X ={1,2 }. The number of different ordered pairs(Y,Z) that can be formed such that Y and Z are subsets of X and Y intersection Z is empty, is?..
Please, solve this manually, means i need those subsets and ordered pairs..

Grade:12

1 Answers

Rajat
213 Points
4 years ago
Number of subsets of X = 22=4
Which are \phi, {1}, {2}, {1,2}
Say Y= \phi
Then Z can be {1},{2},{1,2}
Thus we get 3 ordered pairs
Similarly 3 more when Z= \phi
In total 6 when either Y or Z is phi.
Now let the cases when none of them is phi.
None of them can be {1,2} since intersection is null.
Therefore only two possibilities of (X,Y)
= ({1},{2}) or ({2},{1})
In total we can have 3+3+2= 8 ordered pairs 
Kindly upvote!

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